How can I manually assign individual vertex UV coordinates?
You can edit the uv manually in the UV/Image Editor.
After marking seams and unwrapping, open up the UV Editor.
If you check Normalized, you can select vertices and input their coordinates in the range of 0 - 1.
When you check the Keep UV and edit mode selection in sync button , the 3D View selection is the same as the UV editor selection.
You could select vertices in the 3D View and input their uv coordinates in the UV editor.
Note, that you can also use the standard select, grab, rotate and scale tools in the 2D space of the UV editor.